Erratum

The updated original online version for this chapter can be found at 10.1007/978-3-319-18539-2_17

In the original publication on page vi, there is a typographical error in the print and online versions of this book. “Principal” was incorrectly spelled as “Principle.”

Corrections to chapter 17, page 381, follow, and these changes have been updated in the book.

Chapter 17

Statistical Methods Used in Interim Monitoring

p 381

Many different spending functions can be specified. The O’Brien–Fleming α₁(t*) and Pocock α₂ (t*) type spending functions are specified as follows:

$$ \begin{array}{ll}{\alpha}_1\left(t^{*}\right)=2-2\Phi \left({Z}_{\alpha / 2}/\sqrt{t^{*}}\right)\hfill & \sim \mathrm{O}'\mathrm{Brien}\hbox{-} \mathrm{Fleming}\hfill \\ {}{\alpha}_2\left(t^{*}\right)=\alpha\ \ln \left(1+\Big(e-1\right)t^{*}\Big)\hfill & \sim \mathrm{Pocock}\hfill \\ {}{\alpha}_3\left(t^{*}\right)=\alpha\ {t^{*}}^{\theta}\hfill & \mathrm{for} \ \theta >0\hfill \end{array} $$

The spending function α₃(t*) spends alpha uniformly during the trial for θ = 1, at a rate somewhat between α₁(t*) and α₂(t*). Other spending functions have also been defined [75, 76].